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# Course List   ## Complex Variable and Special Functions (Math 5)

• Course Code :
MTH 311
• Level :
• Course Hours :
3.00 Hours
• Department :
Department of Mechanical Engineering

## Area of Study :

To familiarize students with the basic concepts of Complex Variable and Special Functions and to make them able to develop an understanding of mathematical concepts that provide a foundation for the mathematics encountered in Engineering. The course allows students to work at their own level there by developing confidence in mathematics and general problem solving. On successful completion of this course the student will be able to: 1. demonstrate a sound understanding of a number of mathematical topics that are essential for studies in Engineering; 2. interpret and solve a range of problems involving mathematical concepts relevant to MTH 311; 3. Effectively communicate the mathematical concepts and arguments contained in this course.

## a. Knowledge and Understanding:

 1- Provide a through understanding and working knowledge of mathematics relevant to this course 2- Develop techniques for solving problems that may arise in every day life

## b. Intellectual Skills:

 1- Demonstrate knowledge of the theory, concepts, methods,and techniques of Complex variables and Special Functions, and ordinarily equations 2- Think logically 3- Rules and solve problems 4- Organize tasks into a structured form 5- Evaluate the evolving state of knowledge in a rapidly developing area 6- Transfer appropriate knowledge and methods from one topic within the subject to another

## c. Professional and Practical Skills:

 1- Understand Function of a complex variable and elementary functions 2- Understand the analytically, Cauchy Riemann equations and Complex integrals 3- Know the Taylor and Laurent series and be able to evaluation real integrals by residues 4- The relationship between Gamma and Beta functions and be able to calculate integrals 5- Understand conformal Mapping and be able to calculate integrals 6- Know Bessel’s functions and be able to calculate the solution of differential equation 7- Understand the definitions and types of partial differential equations 8- Understand D’fflambert solution of Wave Equation and Separation of variables for Heat Equation and be able to determine a unique solution. But first we will relate the canonical forms to equations describing physical phenomena. 9- know Finite difference method for partial solutions of differential equations

## d. General and Transferable Skills:

 1- Gain the principle of quality control 2- Develop skills related to creative thinking, problem solving

## Course topics and contents:

Topic No. of hours Lecture Tutorial/Practical
Functions of a complex variable: Elementary functions, analytically, Cauchy-Riemann equations. 10 6 4
Complex Integrals: Cauchy Integral formula, Taylor and Laurent series 10 6 4
Cauchy Residues Theorem (Evaluation of real integrals by residues), Conformal Mapping 2 2 0
First Exam 5 3 2
Special functions: Gamma and Beta functions, Bessel functions and Legendre polynomials, power series solution of ordinary differential equations 16 12 4
Partial differential equation: Definitions and types, solution of Wave Problem 16 12 4
Second Exam 3 1 2
Heat Equation, Laplace’s equations in different systems of coordinates, and Finite difference method for partial solutions of differential equations 16 12 4
Final Exam 2 2 0

## Teaching And Learning Methodologies:

Teaching and learning methods
Lectures
Tutorial
Class discussions and activities
Homework and self-study

## Course Assessment :

Methods of assessment Relative weight % Week No. Assess What
Assignments and quizzes 20.00 1
Attendance and Participation 10.00 1
Final-term Exam 40.00 16 To assess overall understandings, concepts, Knowledge, Problem solving, and mathematical skills delivered by the course
First Exam 15.00 7 To assess the levels of math skills needed for successful completion of the course, and to improve teaching and learning for all students
Second Exam 15.00 12 To assess comprehension, Knowledge, Problem solving, and mathematical skills delivered by the course after 6 weeks of studying

## Books:

Book Author Publisher
Advanced Engineering Mathematics Warren S. Wright, Dennis G. Zill Jones & Bartlett Learning

## Course notes :

Course notes & handouts

## Recommended books :

Advanced Engineering Mathematics, Dennis G. Zill, warrens. Wright, Michael R, Cullen, Fourth Edition, 2011